ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT …rp.bergen.org/cms/lib01/NJ01001874/Centricity/Domain/117/Math 6-8...ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT Math 6-8 Curriculum Guide ... the

ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT

Math 6-8 Curriculum Guide

BOE Approval: 02/12/2015

2

ROCEHELLE PARK TOWNSHIP SCHOOL DISTRICT

Math 6-8 Curriculum Guide

Table of Contents

DTSD Mission Statement 3

Department Vision 3

Affirmative Action Compliance Statement 3

Curriculum and Planning Guides

Grade 6 Units 4 - 18



STANDARDS FOR MATHEMATICAL PRACTICE

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels

should seek to develop in their students. These practices are integrated throughout our curriculum at all grade

levels.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate Tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

INTERDISCIPLINARY THEMES

Planned interdisciplinary activities can help students to make sensible connections among subjects, while

limiting the specialist's tendency to fragment the curriculum into isolated pieces. Such activities provide

students with broader personal meaning and the integrated knowledge necessary to solve real-world problems.

Teachers are encouraged to independently and cooperatively develop lessons which cover multiple areas

simultaneously.

3

MISSION STATEMENT

The Rochelle Park School District’s envisions an educational community which inspires and empowers all

students to become self-sufficient and thrive in a complex, global society

DEPARTMENT VISION

It is the firm belief of the Rochelle Park Township School District that mathematics provides students with a

common language that allows them to actively participate in collaborative problem solving scenarios. This

common language will provide our students with a foundation of a deeper understanding of their future fiscal

responsibilities within the global economy they participate in. We encourage our students to advocate for their

communities by acting as a driving force, so that we may build a more sustainable economy in the future.

This guide is to provide focus for the learning that will take place in this course, but is completely modifiable

based upon the needs and abilities of the students and their Individual Education Plans. Curriculum

implementation follows best practice and adheres to the New Jersey Core Content Standards. At the same time,

for students with disabilities, the Individual Education Plan, specifically the Goals and Objectives of the plan,

supersede any curricular adherence or suggestion.

21ST

CENTURY THEMES & SKILLS

Embedded in much of our units of study and problem based learning projects are the 21st Century Themes as

prescribed by the New Jersey Department of Education. These themes are as follows:

Global Awareness

Financial, Economic, Business, and Entrepreneurial Literacy

Civic Literacy

Health Literacy

AFFIRMATIVE ACTION COMPLIANCE STATEMENT

The Rochelle Park Township Public Schools are committed to the achievement of increased cultural awareness,

respect and equity among students, teachers and community. We are pleased to present all pupils with

information pertaining to possible career, professional or vocational opportunities which in no way restricts or

limits option on the basis of race, color, creed, religion, sex, ancestry, national origin or socioeconomic status.

4


Math Curriculum Guide

Grade: 6 Unit: Operations and Properties (1) Time Frame: 20.5 periods

ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS

Estimation can be used to check the

reasonableness of answers.

Many mental math strategies use number

properties that you already know to make

equivalent expressions that may be easier to

simplify.

What is the Order of Operations and how does it

help?

How are exponents used to represent numbers and

why?

How do I use the commutative, associative, and

distributive property to solve equations and

expressions?

KNOWLEDGE SKILLS STANDARDS

Students will know:

dividing multi-digit numbers can be

done using the standard algorithm.

numerical expressions can be

written using whole number

exponents.

in expressions, letters stand for

numbers.

properties of operations can be used

to generate equivalent expressions.

expressions can be evaluated with

specific values for variables using

the conventional order of

operations.

different strategies to find the

greatest common factor and least

common multiple of two whole

numbers.

the sum of two whole numbers can

be expressed with a common factor

as a multiple of a sum of two whole

numbers with no common factor

using the distributive property.

Students will be able to:

use the order of operations.

use properties to find

equivalent expressions.

(1) estimate with whole numbers.

(2) use the algorithm for division

and interpret the quotient and

remainder in a real world

setting.

(3) represent numbers by using

exponents.

(4L)-use a graphing calculator to

explore the order of operations.

(4) use the order of operations.

(5) use number properties to

compute mentally.

(2) CC.6.NS.2

(3) CC.6.EE.1

(4L) CC.6.EE.2,2c

8.1.8.A.5

(4) CC.6.EE.2,2c

(5) CC.6.EE.3

CC.6.NS.4

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT

estimate, compatible number,

underestimate, overestimate, dividend,

divisor, exponent, base, exponential

form, numerical expression, simplify,

order of operations, commutative

property, associative property,

distributive property

Holt McDougal Mathematics 6:

Chapter 1

HMM 6 Lab Activities WB (3)

Countdown to Mastery: Do Now

graphing calculator (4L)

number cubes (5)

Formative:

Observation

Quiz 1A

Quiz 1B

Summative:

Chapter 1 Test

5



Grade: 6 Unit: Introduction to Algebra (2) Time Frame: 28 periods


An equation is a mathematical statement that two

expressions are equal.

Multiplication and division are inverse operations

as addition and subtraction are inverse operations.

Why should we study Algebra?

What are mathematical expressions and equations?

What is the difference?

How do I determine whether a solution to an

equation is correct?


Students will know:

in expression, letters stand for

numbers.

parts of expressions can be identified

using mathematical parts and one or

more parts can be viewed as a single

entity.

operations with numbers and/or

variables can be written as

expressions.

solving an equation or inequality is a

process of answering the question

“which values from a specified set, if

any, make the equation or inequality

true?

methods to identify when two

expressions are equivalent.

real world and mathematical

problems can be solved by writing

and solving equations of the form x +

p = q and px = q where p,q, and x are

all nonnegative rational numbers.

variables can be used to represent an

unknown number or a number in a

specified set and that expressions can

be written when solving a real-world

or mathematical problem.


write expressions and

equations for given situations.

evaluate expressions.

solve one-step equations.

(1) identify and evaluate

expressions.

(2) translate between words and

math.

(3) write expressions for tables

and sequences.

(3L)- use grid paper to model the

area and perimeter of different

rectangles.

(4) determine whether a number

is a solution of an equation.

(5) solve whole number addition

equations.

(6) solve whole number

subtraction equations.

(7) solve whole number

multiplication equations.

(8) solve whole number division

equations.

(1) CC.6.EE.2,2b

(2) CC.6.EE.2,2a,2b

(3) CC.6.EE.2,2a

(3L) CC.6.EE.2,3

(4) CC.6.EE.4,5

(5) CC.6.EE.6,7

(6) CC.6.EE.6

(7) CC.6.EE.6,7

(8) CC.6.EE.6


algebraic expression, constant, equation,

evaluate, inverse operations, solution,

variable


Chapter 2

HMM 6 Lab Activities WB

(1,5,7)


grid paper (3L), scissors (3L),

balance scales (4,6), algebra

tiles/counters(5), index cards (8)

Formative:

Observation

Quiz 2A

Quiz 2B

Summative:

Chapter 2 Test

6



Grade: 6 Unit: Decimals (3) Time Frame: 29.5 periods


Decimal numbers represent combinations of whole

numbers and numbers between whole numbers.

Equations with decimals can be solved using

inverse operations just as equations with whole

numbers can be solved using inverse operations.

How can I add, subtract, multiply and divide

decimals fluently?

How do decimal numbers impact multiplication

and division?

How do I estimate with decimals?


Students will know:

adding, subtracting,

multiplying, and dividing

decimals can be done using

the standard algorithm for

each operation.


problems can be solved by

writing and solving equations

of the form x + p = q and

px=q where p, q, and x are all

nonnegative rational

numbers.

variables can be used to

represent an unknown

number or a number in a

specific set and that

expressions can be written

when solving a real world or

mathematical problem.


use common procedures to

multiply and divide decimals.

evaluate expressions and solve

equations with decimals.

(1) write, compare, and order

decimals using place value and

number lines.

(2) estimate decimal sums,

differences, products, and

quotients.

(3L) use decimal grids to model

addition and subtraction of decimals.

(3) add and subtract decimals.

(4L) use decimal grids to model

multiplication and division of

decimals.

(4) multiply decimals by whole

numbers and by decimals.

(5) divide decimals by whole

numbers.

(6) divide whole numbers and

decimals by decimals.

(7) solve problems by interpreting the

quotient.

(8) solve equations involving

decimals

(3L) CC.6.NS.3

(3) CC.6.EE.7

CC.6.NS.3

(4L) CC.6.NS.3

(4) CC.6.EE.7

CC.6.NS.3

(5) CC.6.NS.3

(6) CC.6.NS.3

(7) CC.6.NS.3

(8) CC.6.EE.6,7


clustering, front-end estimation


Chapter 3

HMM 6 Lab Activities WB (3,6,8)


decimal grids/grid paper (3L, 4L),

colored pencils (4L), transparency

grids (4L), graph paper (5), index

cards (6)

Formative:

Observation

Quiz 3A

Quiz 3B

Summative:

Chapter 3 Test

7



Grade: 6 Unit: Number Theory & Fractions (4) Time Frame: 29.5 periods


You can use factors to write a number in different

ways.

Algebraic expressions can be factored using GCF

and the distributive property.

Decimals and fractions can often be used to

represent the same number.

How can we develop and apply number theory

concepts in problem solving situations?

What do the factors and multiples of a number tell

me?

How do we identify and demonstrate knowledge of

fractions?


Students will know:

the greatest common factor of

two whole numbers less than or

equal to 100 can be found and

the sum of two whole numbers

1-100 can be expressed using

the distributive property.

expressions can be identified as

equivalent when they are

named the same number

regardless of the value

substituted into them.

rational numbers can be ordered

and also have an absolute value.


view a fraction as parts of a

whole.

use multiplication and division

to determine equivalent

fractions.

(1) write prime factorizations of

composite numbers.

(2) find the greatest common factor

(GCF) of a set of numbers.

(2L) use a graphing calculator to

find the greatest common

factor (GCF) of two or more

numbers.

(3) factor numerical and algebraic

expressions and write

equivalent numerical and

algebraic expressions.

(4L)use decimal grids to show the

relationship between decimals

and fractions.

(4) convert between decimals and

fractions.

(5L) use pattern blocks to model

equivalent fractions.

(5) write equivalent fractions.

(6) covert between mixed numbers

and improper fractions.

(7) use pictures and number lines

to compare and order fractions.

(2) 6.NS.4

(2L) 6.NS.4

8.1.8.A.5

(3) 6.EE.4

(7) 6.NS.7

8


common denominator, coefficient,

equivalent expressions, equivalent

fractions, factor, greatest common

factor, improper fraction, like

fractions, mixed numbers, prime

factorization, proper fraction,

repeating decimal, simplest form,

term, terminating decimal, unlike

fractions


Chapter 4

HMM 6 Lab Activities WB (6,7)


graphing calculator (2L), decimal

grids/grid paper (4L), fraction bars

(4L, 5L, 6, 7), pattern blocks (5L),

number cubes (5L), customary

rulers (5L, 6), transparency ruler

(5L)

Formative:

Observation

Quiz 4A

Quiz 4B

Summative:

Chapter 4 Test

9



Grade: 6 Unit: Fraction Operations (5) Time Frame: 26.5 periods


You can use any common denominator or the least

common denominator to add and subtract unlike

fractions.

Reciprocals are necessary to divide by fractions.

How do I add, subtract, multiply, and divide

fractions fluently?

How can I solve equations with fractions?


Students will know:

word problems can be solved

using division of fractions.

the greatest common factor of

two whole numbers less than or

equal to 100 can be found and

the sum of two whole numbers

1-100 can be expressed using

the distributive property.

real world problems can be

solved by writing and solving

equations in the form x+p=q

and px=q where all values are

nonnegative rational numbers.


understand the procedures for

multiplying dividing fractions.

evaluate expressions and solve

equations with fractions.

(1) find the least common multiple

(LCM) of a group of numbers.

(2) add and subtract fractions with

unlike denominators.

(3) Regroup mixed numbers to

subtract.

(4) Solve equations by adding and

subtracting fractions.

(5) Multiply mixed numbers.

(5L) use grids to model division of

Fractions.

(5L) use fraction bars to model the

division of fractions in world

problems.

(6) divide fractions and mixed

numbers.

(7) solve equations by multiplying

and dividing fractions.

(1) 6.NS.4

(4) 6.EE.7

(5L)6.NS.1

(5L)6.NS.1

(6) 6.NS.1

(7) 6.EE.7

6.NS.1


least common denominator, least

common multiple, reciprocals,

multiplicative inverse


Chapter 5



spinners (1), fraction bars (2,3),

grid paper (2, 3, 5L), fraction bar

transparency (2,3), transparency

grid (5L)

Formative:

Observation

Quiz 5A

Quiz 5B

Summative:

Chapter 5 Test

10



Grade: 6 Unit: Data Collection and Analysis (6) Time Frame: 29.5 periods


Descriptions of a set of data are called mean,

median, mode, and range.

Data can be displayed on various plots.

How can data be described using mean, median,

mode, and range?

Which representation is best for analyzing the

distribution of data?

How can I use the appropriate measure of central

tendency or variability to analyze or describe a

data set?


Students will know:

a statistical question anticipates

variability in data related to the

question and that it needs to be

accounted for in answers.

data collected to answer a

statistical question has a

distribution which can be

described in various different

ways.

a measure of accentor for a

numerical data set summarizes

all of its values with a single

number, while a measure of

variation describes how its

values vary with a single

number.

the numerical data can be

displayed in plots on a number

line, including dot plots, box

plots, and histograms.

numerical data sets can be

summarized in relation to their

context.


use mean, median, mode, and

range to summarize data sets.

make and interpret a variety of

graphs.

(1L) collect data and use counters

to find the mean of a set of

data.

(1) find the range, mean, median and

mode of a set of data.

(2) learn the effect of additional data

and outliers.

(3) calculate, interpret, and compare

measures of variation in a data set.

(4) organize data in line plots,

frequency tables and histograms.

(4L) use a survey to collect and

organize data into a table.

(4E) describe the frequency

distribution of a data set and

make a cumulative frequency

table and histogram.

(5) describe and compare data

distributions by their center,

spread, and shape, using box and

whisker plots or dot plots.

(1L) 6.SP.2

(1) 6.SP.3

6.SP.2

(2) 6.SP.3

(3) 6.SP.1

6.SP.3

6.SP.4

(4) 6.SP.4

(4L) 6.SP.5

(4E) 6.SP.5

6.SP.2

(5) 6.SP.5

6.SP.2

6.SP.3

6.SP.4


box and whisker plot, frequency,

frequency table, histogram,

interquartile range (IQR), line plot,

mean, median, mode, outlier,

quartiles, range, variation


Chapter 6



counters (1L)

magazines/newspapers (2)

graph paper (6L)

Formative:

Observation

Quiz 6A

Quiz 6B

Summative:

Chapter 6 Test

11



Grade: 6 Unit: Proportional Relationships (7) Time Frame: 32.5 periods


Scale models use proportional relationships to

make smaller versions of large objects and larger

versions of small objects.

Ratios can be written to compare a part to a part, a

part to the whole, or the whole to a part.

Ratios in tables can be used to make estimates or

predictions.

One number can be represented in three different

forms: fraction, decimal, and percent.

How are ratios and rates connected?

How are fractions, decimals, and percents related?

What techniques can be used to find fraction,

decimal or percent names for the same quantities?


Students will know:

a unit rate can be associated with

a ratio a:b and that rate language

can be used in the context of a

ratio relationship.

real-world and math problems can

be solved using rate and ratio

reasoning through tables of

equivalent ratios, tape diagrams,

double number line diagrams, or

equations.

a rational number is a point on a

number line and that number line

diagrams and coordinate axes can

be extended with negative number

coordinates.

integers and other rational

numbers can be positioned on a

horizontal or vertical number line

diagram and on a coordinate

plane.

the relationship between two

quantities can be described by

using a ratio and ratio language.

a percent of a quantity can be

found as a rate per 100 and that

problems can be solved given a

part and the percent when being

asked to find the whole.


use tables to determine

whether quantities are in

equivalent ratios.

Use proportional reasoning to

solve rate and ratio problems.

(1) write ratios and rates and find

rates.

(2) use a table to find equivalent

ratios and rates.

(3) graph ordered pairs on a

coordinate grid.

(3E) graph equivalent ratios on

the coordinate plane.

(4L) use counters to model

equivalent ratios.

(4) write and solve proportions.

(5L) use a 10 by 10 grid to model

a

percent.

(5) write percents as decimals

and fractions.

(6) write decimals and fractions

as percents.

(7) find the percent of a number.

(8) solve problems involving

percents.

(1) 6.RP.2

(2) 6.RP.3

(3) 6.NS.6

6.NS.6c

(3E)6.RP.3

(4L)6.RP.1

(4) 6.RP/1

(5L)6.RP.3c

(5) 6.RP.3c

(6) 6.RP.3c

8.1.8.A.5

(7) 6.RP.3

6.RP.3c

(8) 6.RP.3

12


coordinate grid, equivalent ratios,

ordered pair, percent, proportion, rate,

ratio, unit rate


Chapter 7


(3,5,7)


graphing calculator (6)

colored pencils (2)

graph paper (3, 5L, 7)

road maps (3)

two color counters (4L)

10 by 10 grids (5L)

number cubes (5)

media advertisements involving

percents (7)

Formative:

Observation

Quiz 7A

Quiz 7B

Summative:

Chapter 7 Test

13



Grade: 6 Unit: Measurement & Geometry (8) Time Frame: 29.5 periods


Conversion factors are an efficient tool for

converting units.

In the same way that the area of a plane figure is

the number of non-overlapping unit squares

needed to cover the figure, the volume of a three-

dimensional figure is the number of non-

overlapping unit cubes needed to fill the figure.

What attributes of a shape are important to

measure?

How do I determine a basic shape and the

appropriate formula to find area, perimeter, and

volume?

What am I finding when I find area and perimeter?


Students will know:

ratio reasoning can be used to

convert measurement units and

that units can be appropriately

manipulated or transformed

when multiplying or dividing

quantities.

the area of right triangles, other

triangles, special quadrilaterals,

and polygons can be found by

composing into rectangles or

decomposing into triangles and

other shapes and that these

techniques can be used to solve


problems.

expressions can be evaluated at

specific values of their

variables including expressions

that arise from formulas used in

real world problems.

arithmetic operations should be

performed in the conventional

order when there are no

parentheses to specify a

particular order.

volume of a right rectangular

prism with fractional edge

lengths can be found by

packing it with unit cubes of the

appropriate unit fraction edge

lengths and that the volume is

the same as would be found by


solve problems that involve

lengths, areas, and volumes.

use fractions and decimals to

solve measurement problems.

(1) convert customary units of

measure.

(2) convert metric units of

measure.

(3) estimate the area of irregular

figures and find the area of

rectangles and parallelograms.

(3L) use grid paper to discover the

relationship between the area

of a square and its side length.

(4) find the area of triangles and

trapezoids.

(4L) use geometry software to

explore area.

(5) break a polygon into simpler

parts to find its area.

(6L) use centimeter cubes to

explore the volume of prisms.

(6) estimate and find the volumes

of rectangular prisms and

triangular prisms.

(7L) use a net to build a three-

dimensional figure.

(7) find the surface areas of prisms,

pyramids, and cylinders.

(1) 6.RP.3d

(2) 6.RP.3d

(3) 6.G.1

6.EE.2c

(4) 6.G.1

(4L) 8.1.8.A.5

(5) 6.G.1

(6L) 6.G.2

(6) 6.G.2

6.EE.2c

(7L) 6.G.4

(7) 6.G.4

14

multiplying the edge lengths of

the prism.


problems involving volume can

be solved by applying the

rectangular prism volume

formula.

that three dimensional figures

can be represented using nets

made up of rectangles and

triangles and that these nets can

be used to find the surface area

which can be applied to real-

world and mathematical

problems.


area, net, surface area, volume


Chapter 8


(1,2,4,6,7)


geometry software (4L)

map of Australia (3L)

graph paper (3, 7L)

grid paper (3L)

centimeter cubes (6L)

centimeter graph paper (6L)

prism models (6)

scissors (7L)

tape (7L)

Formative:

Observation

Quiz 8A

Quiz 8B

Summative:

Chapter 8 Test

15



Grade: 6 Unit: Integers & the Coordinate Plane (9) Time Frame: 20.5 periods


Integers and their absolute values are useful in

finding and comparing distances.

Understanding a coordinate plane can prove useful

in everyday life. For example, we use a coordinate

system on Earth to find exact locations.

What ordered pair corresponds to a given point on

a graph?

How does reversing the order of the numbers

affect the location of the point?

What is absolute value?

Where do we see integers in the real world?


Students will know:

positive and negative numbers

are used together to describe

quantities having opposite

directions or values and that

positive and negative numbers

can be used to represent

quantities in real world

contexts.

the order and absolute value of

rational numbers.

statements of inequality can be

interpreted as statements about

the relative position of two

numbers on a number line

diagram.

statements of order for rational

numbers can be written,

interpreted, and explained in

real world contexts.

a rational number is a point on

a number line and that number

line diagrams and coordinate

axes can be extended with

negative number coordinates.

integers and other rational

numbers can be positioned on a

horizontal or vertical number

line diagram and on a

coordinate plane.

polygons can be drawn in the

coordinate plane given

coordinates for the vertices and

that coordinates can be used to

find the length of a side joining


use negative numbers in

everyday contexts.

draw and transform figures in

the coordinate plane.

(1) identify and graph integers and

find opposites.

(2) compare and order integers.

(2E) compare and order negative

rational numbers.

(3) locate and graph points on the

coordinate plane.

(4) draw polygons in the coordinate

plane and find the lengths of

their sides.

(5) use translations, reflections, and

rotations to change the

positions of figures in the plane.

(1) 6.NS.5

(2) 6.NS.7

6.NS.7a

6.NS.7b

(2E) 6.NS.6

6.NS.6c

(3) 6.NS.6

(4) 6.G.3

6.NS.6

6.NS.6c

6.NS.8

(5) 6.NS.8

6.NS.6b

6.NS.6c

16

points with the same first or

second coordinate.


problems can be solved by

graphing points in all four

quadrants of the coordinate

plane and that coordinates and

absolute value can be used to

find distances between points

with the same first or second

coordinate.

signs of numbers in ordered

pairs are indicating locations in

quadrants of the coordinate

plane and that when two

ordered pairs differ only by

signs, the locations of the points

are related by reflections across

one or both axes.


absolute value, axes, coordinate

plane, coordinates, integer, linear

equation, negative number,

opposites, origin, positive number,

quadrants, x-axis, x-coordinate, y-

axis, y-coordinate


Chapter 9



two colored counters (1)

large sticky notes (2)

graph paper (3)

state maps (3)

grid paper (5)

pattern blocks (5)

Formative:

Observation

Quiz 9A

Quiz 9B

Summative:

Chapter 9 Test

17



Grade: 6 Unit: Functions (10) Time Frame: 17.5 periods


A function is one way of using mathematics to

describe an observable event.

Functions, which show how different values are

related, can be used in math to describe the real

world.

How do variables relate to functions?

How do I graph a linear equation or inequality?


Students will know:

variables can be used to represent

two quantities in a real-world

problem that change in

relationship to one another and

that an equation can be written to

express one quantity thought of as

the dependent variable, in terms

of the other quantity thought of as

the independent variable. Also,

that graphs and tables can be used

to analyze the relationship

between the dependent and

independent variables.

real world and math problems can

be solved using rate and ratio

reasoning through tables of

equivalent ratios, tape diagrams,

or equations.

tables can be made of equivalent

ratios relating quantities with

whole number measurements and

that once the missing values are

found in the tables, they can then

be plotted on the coordinate

plane.

an inequality in the form of x>c

or x<c can be written to represent

a constraint or condition in a real-

world or mathematical problem

and that inequalities of the form

x>c or x<c have infinitely many

solutions which can be

represented on number line

diagrams.


use equations to describe

relationships shown in a

table.

write inequalities to describe

certain situations.

(1) use data in a table to write an

equation for a function and

use the equation to find a

missing value.

(2) represent linear functions

using ordered pairs and

graphs.

(2E) identify the independent and

dependent variables in a real

world situation.

(3) find rates of change and

slope.

(4) read and write inequalities

and graph them on a number

line.

(1) 6.EE.9

(2) 6.EE.9

(2E) 6.EE.9

(3) 6.RP.3

6.RP.3a

(4) 6.EE.8

18


algebraic inequality, compound

inequality, function, inequality, input,

linear equation, output, rate of

change, slope, solution of an

inequality


Chapter 10


(1,2,3)


graph paper (2)

square tiles (3)

graph paper (3)

uncooked spaghetti (3)

Formative:

Observation

Summative:

Chapter 10 Test

19



Grade: 7 Unit: Algebraic Reasoning (1) Time Frame: 18 periods


Just as the order of the words in a sentence is

important to the sentences meaning, the order of

operations is essential to the meaning or value of a

mathematical expression.

The Commutative Property and the Associative

Property are cornerstones for the study of

Mathematics.

How is thinking algebraically different from

thinking arithmetically?

How do I use the rules for Order of Operations to

solve expressions?

KNOWLEDGE SKILLS NJCCCS

Students will know:

a horizontal or vertical number

line diagram can be used to add

and subtract rational numbers.

strategies to add and subtract

rational numbers such as

operational properties.

strategic tools to solve multi-

step, real life and mathematical

problems posed with positive

and negative rational numbers.

that re-writing expressions in

different forms can shed light

on a problem and how the

quantities in it are related.


represent real-world or

mathematical problems.

strategies to add, subtract,

factor and expand linear

expressions with rational

coefficients.


use of properties of arithmetic

and properties of equality.

write and simplify expressions

to solve problems.

(1) use the order of operations to

simplify numerical expressions.


evaluate expressions with

exponents.

(2) identify properties of rational

numbers and use them to

simplify numerical expressions.

(3) evaluate algebraic expressions.

(4) translate words into numbers,

variables, and operations.

(5) simplify algebraic expressions.

(1L) 8.1.8.A.5

(2) CC.7.NS.1,1d

CC.7.EE.3

(4) CC.7.EE.2,4

(5) CC.7.EE.1,4


numerical expression, order of

operations, communicative

property, associative property,

identity property, distributive

property, variable, constant,

algebraic expression, evaluate,

term, coefficient


Chapter 1



scientific/graphing calculator (1L)

algebra tiles (5)

Formative:

Observation

Quiz 1A

Quiz 1B

Summative:

Chapter Test 1

20



Grade: 7 Unit: Integers and Rational Numbers (2) Time Frame: 31 ½ periods


The sign of an integer tells its direction, and the

absolute value tells its magnitude.

Integers are closed under the operations of addition

and subtraction, which means that adding or

subtracting any two integers, will produce another

integer.

The Properties of Equality are used to transform an

equation into an equivalent equation whose

solution can be easily seen.

What are integers?

What are rational numbers?

How is the understanding of positive and negative

rational numbers, their representations, and

relationships essential in problem solving?


Students will know:

extensions of previous

understanding of addition and

subtraction to add and subtract

rational numbers.

that real world and

mathematical problems can be

solved with the four operations

involving rational numbers.

p+q as the number located a

distance /q/ from p, in the

positive or negative direction

depending on whether q is

positive or negative.

a number and its opposite have

a sum of zero.

real-world contexts can be

described by sums of rational

numbers.


step, real-life and mathematical



situations in which opposite

quantities combine to make

zero.

subtraction of rational numbers

as adding the additive inverse

p – q = p + (-q).


add, subtract, multiply, and

divide integers.

express fractions as decimals.

(1) compare and order integers and

determine absolute value.

(2L) use integer chips to model

integer addition.

(2) add integers.

(2E) use additive inverses and

absolute value in real-world

situations.


integer subtraction.

(3) subtract integers.


integer multiplication and

division.

(4) multiply and divide integers.

(5L) use algebra tiles to model and

solve equations that contain

integers.

(5) solve one-step equations that

contain integers.

(6) write fractions as decimals, and

vice versa, and determine

whether a decimal is

terminating or repeating.

(7) compare and order fractions

and decimals.

(2L) CC.7.NS.1,3

(2) CC.7.NS.1,1b,3

CC.7.EE.3

(2E) CC.7.NS.1,1a,1b

(3L) CC.NS.1,3

(3) CC.7.NS.1,1c

(4L) CC.7.NS.2,3

(4) CC.7.NS.2

CC.7.EE.2

(5L) CC.7.EE.4

(5) CC.7.EE.4

CC.7.NS.1b

(6) CC.7.NS.2c, 3

(7) CC.7.NS.2c, 3

21

the distance between two

rational numbers on the number

line is the absolute value of

their difference and this

principle as it applies in real

world contexts.


understanding of multiplication

and division and of fractions to

multiply and divide rational

numbers.

expressions in different forms

can shed light on a problem and

how the quantities in it are

related.


represent quantities in a real-

world or mathematical problem.

simple equations and

inequalities can be constructed

to solve problems by reasoning

about the quantities.

properties of operations as

strategies to multiply and divide

rational numbers.


absolute value, additive inverse,

integer, opposite, rational number,

repeating decimal, terminating

decimal


Chapter 2



integer chips (1, 2L, 3L, 4L)

algebra tiles (5L)

colored pencils (5L)

Formative:

Observation

Quiz 2A

Quiz 2B

Summative:

Chapter 2 Test

22



Grade: 7 Unit: Applying Rational Numbers (3) Time Frame: 27 periods


Many statistics are recorded as decimals. By using

operations with decimals you can determine those

statistics.

When there are different denominators, the

fractions cannot be directly combined because they

are different parts of a whole.

How do I evaluate rational numbers using various

operations?

How does understanding the properties of

operations on positive and negative rationals

provide a basis for understanding more complex

mathematical concepts?


Students will know:




rational numbers.


distance /q/ from p, in the positive

or negative direction depending

on whether q is positive or

negative.

subtraction of rational numbers as

adding the additive inverse,

p – q = p + (-q)

real-world and mathematical

problems can be solved with the

four operations involving rational

numbers.




rational numbers.

multiplication is extended from

fractions to rational numbers by

requiring that operations continue

to satisfy the properties of

operations, particularly the

distributive property, leading to

products such as (-1)(-1)=1 and

the rules for multiplying singed

numbers.


add, subtract, multiply, and

divide rational numbers.

solve equations containing

fractions.

(1) add and subtract decimals.

(2) multiply decimals.

(3) divide decimals.


contain decimals.

(5) add and subtract fractions.

(6) multiply fractions and mixed

numbers.

(7) divide fractions and mixed

numbers.


contain fractions.

(1) CC.7.NS.1,1b,1c,3

(2) CC.7.NS.1,2,2a,3

(3) CC.7.NS.2,2b

(4) CC.7.EE.4

CC.7.NS.2

(5) CC.7.NS.1,1b,1c,3

(6) CC.7.NS.1,2,2a,3

(7) CC.7.NS.2,2b,3

(8) CC.7.EE.4

23

products of rational numbers can

be described in real-world

contexts.

integers can be divided, provided

that the divisor is not zero and

every quotient of integers is a

rational number. If p and q are

integers, then –(p/q) = (-p)/q =

p/(-q).

quotients of rational numbers can

be described in real-world

contexts.

variables can be used to represent

quantities in a real-world or

mathematical problem.

simple equations and inequalities

can be constructed to solve

problems by reasoning about the

quantities.


multiplicative inverse, reciprocal


Chapter 3


(1,6,7)


decimal grids (2)

grid transparencies (2)

graph paper (3,4)

measuring tape (3)

colored pencils (6)

grids (6)

Formative:

Observation

Quiz 3A

Quiz 3B

Summative:

Chapter 3 Test

24



Grade: 7 Unit: Proportional Relationships (4) Time Frame: 24 periods


Proportions can be used to solve real-world

problem situations such as: finding the heights of

objects that are too tall to measure directly, scaling

a recipe, converting between different units of

measurement.

Arithmetically, ratios look and behave like

fractions, but they are not the same as fractions.

A dilation is a proportional shrinking or

enlargement of a figure.

What does it mean to be in a ratio of 3/5?

How can I distinguish between situations that are

proportional or not proportional and use

proportions to solve problems?

How can I apply proportionality to measurement in

multiple contexts, including scale drawings?


Students will know:

unit rates associated with ratios

of fractions, including ratios of

lengths, areas and other

quantities measured in like or

different units.

proportional relationships

between quantities

the constant of proportionality

(unit rate) from tables, graphs,

equations, diagrams, and verbal

descriptions of proportional

relationships

whether two quantities are in a

proportions relationship by

testing for equivalent ratios in a

table or graphing on a

coordinate plane and observing

whether the graph is a straight

line through the origin.

that real world and

mathematical problems can be

solved with the four operations

involving rational numbers.

proportional relationships can

be represented by equations of

the form t = pn or y = kx.

that scale drawings of

geometric figures can be used

to compute actual lengths and

areas as well as to reproduce a


use proportionality to solve

problems, including problems

involving similar objects, units

of measurement, and rates

(1) find and compare unit rates,

such as average speed and unit

price

(2) find equivalent ratios and

identify proportions

(3) solve proportions using cross

products

(4) use ratios to determine if two

figures are similar

(5) use similar figures to find

unknown side lengths

(6) understand ratios and

proportions in scale drawings,

and use ratios and proportions

with scale

(6L1) use graph paper to make

scale drawings and scale

models

(6L2) use scale drawings to find

actual measures of objects and

to create a new drawing of the

object in a different scale

(1) CC.7.RP.1,2,2b

(2) CC.7.RP.2,2a

CC.7.NS.3

(3) CC.7.RP.1,2,2c

(4) CC.7.RP.2,2c

CC.7.NS.3

(5) CC.7.G.1

CC.7.RP.2c

CC.7.EE.2

(6) CC.7.G.1

CC.7.NS.3

(6L1) CC.7.G.1

(6L2) CC.7.G.1

25

scale drawing at a different

scale.




related.


corresponding angles,

corresponding sides, cross product,

equivalent ratios, indirect

measurement, proportion, rate,

scale, scale drawing, scale factor,

scale model, similar, unit rate


Chapter 4


(2,3,4,5,6)


measuring tape (3)

customary rulers (5)

social studies/reference books (6)

measuring tape (6L1)

Formative:

Observation

Quiz 4A

Quiz 4B

Summative:

Chapter 4 Test

26



Grade: 7 Unit: Graphs (5) Time Frame: 18 periods


Graphs can be used to analyze countless real-world

phenomena, such as speed, time, and distance.

A graph is an efficient way of conveying a great

deal of information.

A rate of change is a ratio that compares the

amount of change in a dependent variable to the

corresponding amount of change in and

independent variable.

What story does a line tell?

What makes a pattern linear?

How can I apply proportionality to measurement in

multiple contexts, including speed?


Students will know:

unit rates associated with ratios

of fractions, including ratios of

lengths, areas and other

quantities measured in like or

different units.

proportional relationships

between quantities

whether two quantities are in a

proportions relationship by

testing for equivalent ratios in a

table or graphing on a

coordinate plane and observing

whether the graph is a straight

line through the origin.

the constant of proportionality

(unit rate) from tables, graphs,

equations, diagrams, and verbal

descriptions of proportional

relationships


be represented by equations of

the form t = pn or y = kx.

that a point (x,y) on the graph of

a proportional relationship

means in terms of a situation

with special attention to the

points (0,0) and (1, r) where r is

the unit rate.

a horizontal or vertical number

line diagram can be used to add

and subtract rational numbers.


graph linear relationships and

identify the slope of the line.

identify proportional

relationships (y =kx)

(1) plot and identify ordered pairs

on a coordinate plane

(2) relate graphs to situations

(3L) graph proportional

relationships on the coordinate

plane and use the graph to

determine equivalent ratios and

rates.

(3) determine the slope of a line

and recognize constant and

variable rates of change.

(4) identify, write, and graph an

equation of direct variation.

(3L) CC.7.RP.1,2, 2a,2b,2c

(3) CC.7.RP.1,2d

(4) CC.7.RP.2,2a

CC.7.NS.1

27


constant of variation, coordinate

plane, direct variation, ordered pair,

origin, quadrant, rate of change,

slope, x-axis, y-axis


Chapter 5



graph paper (1, 2, 3L)

media advertisements w/ graphs (2)

Formative:

Observation

Quiz 5A

Quiz 5B

Summative:

Chapter 5 Test

28



Grade: 7 Unit: Percents (6) Time Frame: 22½ periods


Percents are commonly used to express and

compare ratios.

Percent means “per hundred”.

Understanding how to calculate percents has real

world applications in such things are determining

discounts and interest.

Why are fraction, decimal, and percent

equivalencies important?

How can I solve percents problems, involving

discounts, simple interest, taxes, tips and percents

of increase or decrease?


Students will know:








related.


strategies to add and subtract

rational numbers.

multiplication is extended from

fractions to rational numbers by

requiring that operations

continue to satisfy the

properties of operations,

particularly the distributive

property, leading to products

such as (-1)(-1)=1 and the rules

for multiplying singed numbers.

integers can be divided,

provided that the divisor is not

zero and every quotient of

integers is a rational number.

If p and q are integers, then

–(p/q) = (-p)/q = p/(-q).


strategies to multiply and divide

rational numbers.

that proportional relationships


work with proportions

involving percents

solve a wide variety of percent

problems

(1) write decimals and fractions as

percents

(2) estimate percents

(3) use properties of rational

numbers to write equivalent

expressions and equations.

(4) solve problems involving

percent of change

(5) find commission, sales tax and

withholding tax

(6) compute simple interest

(6L) use a calculator to compute

compound interest

(1) CC.7.EE.3

(2) CC.7.EE.3

(3) CC.7.EE.2,3

CC.7.NS.1d,2a,2b,2c

(4) CC.7.RP.3

CC.7.EE.2,3

(5) CC.7.RP.3

(6) CC.7.RP.3

(6L) CC.7.RP.3

8.1.8.A.5

29

can be used to solve multistep

ratio and percent problems.

that re-writing expressions in

different forms can shed light

on a problem and how the

quantities in it are related.




and negative rational numbers;

mental computation and

estimation strategies to convert

between forms and assess the

reasonableness of answers.


commission, commission rate,

interest, percent of change, percent

of decrease, percent of increase,

principal, rate of interest, simple

interest


Chapter 6



dictionaries (1)

toy money (4)

advertisements w/ interest (6)

number cubes (6)

Formative:

Observation

Quiz 6A

Quiz 6B

Summative:

Chapter 6 Test

30



Grade: 7 Unit: Collecting, Displaying, and Analyzing Data (7) Time Frame: 15 periods


Sampling is the area of statistics concerned with

choosing a subset of a population in order to make

statistical inferences about the population as a

whole.

There are various ways of presenting/representing

data both numerically and graphically.

How do I use data to make decisions?

How do I determine the appropriate data display to

organize and communicate findings?


Students will know:

a random sample can be used to

draw inferences about a

population with an unknown

characteristic of interest and to

generate multiple samples (or

simulated samples) of the same

size to gauge the variation in

estimates or predictions.

measures of center and measures

of variability for numerical data

from random samples can be use

to draw informal comparative

inferences about two

populations.

statistics can be used to gain

information about a population

by examining a sample of the

population and that

generalizations about a

population are valid only if the

sample is representative of that

populations. Students will also

understand that random sampling

tends to produce representative

samples and support valid

inferences.

the degree of visual overlap of

two numerical data distributions

with similar variabilities, can be

informally assessed by

measuring the difference

between the centers by

expressing it as a multiple of a

measure of variability.


make and interpret graphs,

such as box-and-whisker plots

make estimates relating to a

population based on a sample

(1) find the mean, median, mode

and range of a data set

(2) display and analyze data in a

box-and-whisker plots


analyze data in box-and-

whisker plots

(3) compare and analyze sampling

methods

(3L1) use a sampling method,

collect data, and summarize

the

results

(3L2) use random sampling to

make predictions about

populations.

(2) CC.7.SP.2,4

(2L) CC.7.SP.4

8.1.8.A.5

(3) CC.7.SP.1

(3L1) CC.7.SP.1,2

(3L2) CC.7.SP.1,2,3

8.1.8.A.5

31


biased sample, box-and-whisker

plot, convenience sample,

interquartile range, lower quartile,

mean, median, mode, outlier,

population, random sample, range,

sample, upper quartile


Chapter 7



graph paper (2)

index cards (2)

graphing calculator (2L, 3)

Formative:

Observation

Summative:

Chapter 7 Test

32



Grade: 7 Unit: Geometric Figures (8) Time Frame: 28 ½ periods


Geometric figures are an integral part of

architecture, industrial design, and construction.

When three side lengths are given, either exactly

one triangle can be formed, or no triangle is

possible.

There are several ways to prove that two triangles

are congruent.

How do we use geometry to make sense of the real

world?

What is the relationship between plane states and

solid states?

What happens to a figure on a coordinate plane

when its vertices are transformed?


Students will know:

facts about supplementary,

complementary, vertical and

adjacent angles to write and

solve simple equations for an

unknown angle in a figure.

that proportional relationships

can be represented by

equations.

various tools/techniques to

draw geometric shapes with

given conditions, while

focusing on the conditions that

determine a unique triangle,

more than one triangle or no

triangle when constructing

triangles from three angle

measures or sides.


use facts about distance and

angles to analyze figures

find unknown measures of

angles

(1) identify and describe geometric

figures

(2L) use a protractor to explore

complementary and

supplementary angles.

(2) identify angles and angle pairs.

(3L1) use a protractor and a

straightedge to find

relationships among the angles

formed by parallel lines and

transversals.

(3) identify parallel, perpendicular,

and skew lines, and angles

formed by a transversal

(3L2) use a compass and a

straightedge to bisect a line

segment, bisect an angle, and

construct congruent angles.

(4) find the measures of angles in

polygons

(5L1) use geometry software to

determine if three given angles

of a triangle determine a unique

triangle, several different

triangles or no triangle.

(5) identify congruent figures and

use congruence to solve

problems

(2L) CC.7.G.5

(2) CC.7.G.5

(3L1) CC.7.G.5

(3) CC.7.G.5

(3L2) CC.7.G.5

(4) CC.7.G.5

CC.7.RP.2c

(5L1) CC.7.G.2

8.1.8.A.5

(5) CC.7.G.2

33


translate and rotate polygons.


determine if three given lengths

of a triangle determine a unique

triangle, several different

triangles, or no triangle.

(5L2) CC.7.G.2

8.1.8.A.5

(5L3) CC.7.G.2

8.1.8.A.5


acute angle, acute triangle, adjacent

angles, angle, complementary

angles, congruent, diagonal, line,

line segment, obtuse angle, parallel

lines, plane, point, ray, right angle,

Side-Side-Side Rule, skew lines,

straight angle, supplementary

angles, transversal, vertex, vertical

angles


Chapter 8


(1,2,3,4)


dot paper (1)

protractors (2, 3L1, 3L2)

cereal/shoe boxes (2)

compasses (3L2)

geometry software (5L1,2,3)

Formative:

Observation

Quiz 8A

Quiz 8B

Summative:

Chapter 8 Test

34



Grade: 7 Unit: Measurement and Geometry (9) Time Frame: 25½ periods


Perimeter and area of a given space can be

determined by measuring their dimensions and

then using a formula. For example, landscapers

rely heavily upon these formulas.

The volume of a three-dimensional figure

represents the amount of space it contains.

Conversion factors can be used to convert one unit

of volume to another.

How many ways can an object be measured?

What does what we measure affect how we

measure?

How are surface area and volume like and unlike

each other?

How do I use a formula to determine surface area

and volume?


Students will know:

formulas for the area and

circumference of a circle and

use them to solve problems; an

informal derivation of the

relationship between the

circumference and area of a

circle.

that rewriting an expression in

different forms in a problem

context can shed light on the

problem and how the quantities

in it are related.

techniques to solve real-world

and mathematical problems

involving area, volume and

surface area of two- and three-

dimensional objects composed

of triangles, quadrilaterals,

polygons, cubes, and right

prisms.

the two-dimensional figures

that result from slicing three-

dimensional figures, as in plane

sections of right rectangular

prisms and right rectangular

pyramids.


solve problems involving area

and circumference of circles

investigate cross sections and

surface area

(1L) use loops of string to explore

perimeter and circumference

(1) find the perimeter of a polygon

and the circumference of a

circle

(2) find the area of the circles

(3) find the area of irregular

figures.

(4) identify various three-

dimensional figures.

(4E) sketch and describe cross

sections of three-dimensional

figures.

(5L) use centimeter cubes to

model and find the volume of

prisms and cylinders.

(5) find the volume of prisms and

cylinders.

(6L) use graph paper to create

two-dimensional nets for three

dimensional figures.

(6) find the surface area of prisms

and cylinders.

(1L) CC.7.G.4

CC.7.EE.2

(1) CC.7.G.4

(2) CC.7.G.4

8.1.8.A.5

(3) CC.7.G.6

(4E) CC.7.G.3

(5L) CC.7.G.6

(5) CC.7.G.6

(6L) CC.7.G.6

(6) CC.7.G.6

35


base, cone, cylinder, edge, face,

lateral area, lateral face, net,

polyhedron, prism, pyramid,

sphere, surface area, vertex,

volume


Chapter 9


(1,2,3,4,5,6)


rulers (1)

string (1)

circular objects (2)

reference books (2)

straight edges (4)

centimeter cubes (5)

prism & cylinder shaped containers

(5)

rice (5)

measuring cups (5)

compasses (6)

circle templates (6)

empty boxes (6)

Formative:

Observation

Quiz 9A

Quiz 9B

Summative:

Chapter 9 Test

36



Grade: 7 Unit: Probability (10) Time Frame: 36 periods


With collected data, you can determine an

experimental probability or predictive outcome.

A probability may be expressed as a ratio, a

decimal, or a percent.

When multiple events are possible, the

probabilities for each event may be equal or

unequal.

What is probability and how do I determine it?

Can I make a prediction about an experiment based

on experimental and theoretical probability?


Students will know:

the degree of visual overlap of

two numerical data

distributions with similar

variabilities, can be informally

assessed by measuring the

difference between the centers

by expressing it as a multiple of

a measure of variability.

that the probability of a chance

event is a number between 0

and 1 that expresses the

likelihood of the event

occurring. Larger numbers

indicate greater likelihood. A

probability near 0 indicates an

unlikely event, a probability

around ½ indicates that an

event is neither likely or

unlikely, and a probability near

1 indicates a likely event.

the probability of a chance

event can be approximated by

collecting data on the chance

process that produces it and

observing its long-run

frequency and predicting the

the approximate relative

frequency given the probability.

understand that, just as with

simple events, the probability

of a compound event is the

fraction of outcomes in the

sample space for which the


understand the meaning of

theoretical probability

use probability and proportions

to make approximate

predictions.

(1) use informal measures of

probability.

(2) find experimental probability.

(3) use counting methods to

determine possible outcomes

(4L1) develop a probability model

for an event with equally likely

outcomes or not equally likely

outcomes.

(4) find the theoretical probability

of an event.

(4L2) use spreadsheets and

calculators to model probability

experiments.

(5L) use manipulatives to calculate

experimental and theoretical

probability.

(5) use probability to predict

events.

(6) find the probability of

independent and dependent

events

(7) find the number of possible

combinations

(8) find the number of possible

permutations

(9) find the probabilities of

compound events

(1) CC.7.SP.3,5,6,8a

(2) CC.7.SP.6,7b

(3) CC.7.SP.7,8b

(4L1) CC.7.SP.6,7b

(4) CC.7.SP.6,8

(4L2) CC.7.SP.7,8c

(5L) CC.7.SP.6,7

(5) CC.7.SP.6,7,7a,7b,8

(6) CC.7.SP.8,8a,8b

CC.7.NS.1b

(7) CC.7.SP.8

(8) CC.7.SP.8

(9) CC.7.SP.8,8a

37

compound event occurs.

a probability model (which may

not be uniform) can be

developed by observing

frequencies in data generated

from a chance process.

a probability model can be

developed and used to find

probabilities of events. Also,

probabilities from a model to

observed frequencies can be

compared; if the agreement is

not good, the source of the

discrepancy can be explained.

methods such as organized lists,

tables and tree diagrams can be

used to represent sample spaces

for compound events.

probabilities for compound

events can be found using

organized lists, tables, tree

diagrams, and simulation.

simulations to generate

frequencies for compound

events.

a uniform probability model

that assigns equal probability to

all outcomes can be used to

determine the probability of

events.


distance /q/ from p, in the

positive or negative direction

depending on whether q is

positive or negative


combination, complement,

compound event, dependent events,

equally likely, event, experiment,

experimental probability, factorial,

fair, Fundamental Counting

Principle, independent events,

outcome, permutation, prediction,

probability, sample space, simple

event, theoretical probability, trial


Chapter 10


(4,6,7,8)


coins (2, 4L1)

colored paper (3)

colored pencils (3)

deck of cards (4L1, 6)

spreadsheet software (4L2)

graphing calculator (4L2)

spinner (6)

index cards (8)

Formative:

Observation

Quiz 10A

Quiz 10B

Summative:

Chapter 10 Test

38



Grade: 7 Unit: Multi-Step Equations & Inequalities (11) Time Frame: 27 periods


When solving equations with variables on both

sides, the goal is to isolate the terms containing

variables on one side of the equation and the

constants on the other side.

Writing and solving an equation is equivalent to

numeric solution methods used when working

backwards.

One of the essential skills of algebra is translating

words into mathematics.

How do you translate problems into equations?

How do you solve for an unknown value in an

equation?

How can I formulate and use different strategies to

solve multi-step equations and inequalities?


Students will know:

strategies to add, subtract,

factor and expand linear

expressions with rational

coefficients.

that variables can be used to

represent quantities in real-

world or mathematical

problems. Also, that simple

equations and inequalities can

be constructed to solve

problems by reasoning about

the quantities.

Word problems can be solved

fluently using equations of the

form px + q = r and

p(x + q) = r. Also, the

comparison of an algebraic

approach to a solution versus

the arithmetic approach and

how they relate to each other

(side-by-side comparison)

word problems that lead to

inequalities of the form

px + q > r and px + q < r. Also,

the solution set of an inequality

can be graphed and interpreted

in the context of the problem.


formulate linear equations in

one variable.

choose procedures to solve

these equations efficiently.


solve two-step equations

(1) solve two-step equations.

(2) solve multi-step equations.

(3) solve equations that have

variables on both sides.

(3E) compare algebraic and

numeric solution methods.

(4) read and write inequalities and

graph them on a number line.

(5) solve one-step inequalities by

adding or subtracting.

(6) solve one-step inequalities by

multiplying or dividing.

(7) solve multi-step inequalities.

(1L) CC.7.EE.1

(1) CC.7.EE.1,4,4a

(2) CC.7.EE.1,4,4a

(3) CC.7.EE.1,4,4a

(3E) CC.7.EE.4,4a

(5) CC.7.EE.4

(6) CC.7.EE.4

(7) CC.7.EE.1,4,4b

39


algebraic inequality, compound

inequality, inequality, solution set


Chapter 11


(2,3,5,6)


algebra tiles (1L, 3, 5)

Formative:

Observation

Quiz 11A

Quiz 11B

Summative:

Chapter 11 Test

40



Grade: 8 Unit: Rational Numbers (1) Time Frame: 30 periods


Rational numbers can be expressed as whole

numbers, integers, fractions, mixed numbers, and

decimals.

The algebraic processes are exactly the same as

those used to solve equations involving integers as

they are to solve linear equations that involve

fractions and decimals.

What makes a number rational?

How is an understanding of rational numbers, their

representations, and relationships useful in

problem solving?

Why is it important for us to know how to solve

equations with rational numbers?


Students will know:

numbers that are not rational

are called irrational.

linear equations can be solved

in one variable.

linear equations with rational

number coefficients can be

solved using the distributive

property and combining like

terms.


multiply and divide rational

numbers.

use the arithmetic of rational

numbers to solve equations.

(1) write rational numbers in

equivalent form.

(2) multiply fractions, mixed

numbers, and decimals.

(3) divide fractions and decimals.

(4) add and subtract fractions with

unlike denominators.

(4L) use graphing calculators to

add and subtract fractions.

(5) solve equations with rational

numbers.


solve two-step equations.

(6) solve two-step equations.

(1) CC.8.NS.1

(4L) 8.1.8.A.5

(5) CC.8.EE.7,7b

(6L) CC.8.EE.7,7b

(7) CC.8.EE.7,7b


rational number, relatively prime,

reciprocal


Chapter 1



Formative:

Observation

Quiz 1A

Quiz 1B

Summative:

Chapter Test 1

41



Grade: 8 Unit: Graphs and Functions (2) Time Frame: 27 periods


Functions will be used in math and science classes,

as well as in many real-world situations.

You can often use functions to describe the

relationship between two quantities

mathematically.

A graph is an efficient way of conveying a great

deal of information.

How do we solve a system of linear equations

graphically?

What is the relationship between graphic and

tabular representations?


Students will know:

by analyzing a graph they can

verbally explain the graph.

a function is a rule that assigns

to each input exactly one

output.

the graph of a function is the set

of ordered pairs (input, output).

strategies to solve linear

equations in one variable.

comparing properties of two

functions can be done in

different ways (algebraically,

graphically).

a function model is a linear

relationship between two

quantities.


use functions to represent,

analyze, and solve problems.

translate among representations

of functions.

(1) write solutions of equations in

two variables as ordered pairs.

(2) graph points on the coordinate

plane.


plot points described by ordered

pairs to adjust graphing window.

(3) interpret information given in a

graph and make a graph to

model a situation.

(4) represent functions with tables,

graphs, or equations.

(5) compare properties of 2

functions and represent in

different ways: algebraically,

graphically, numerically, in

tables or by verbal description.

(5L) use graphing calculators to

generate multiple representations of

a function.

(2L) 8.1.8.A.5

(3) CC.8.F.5

(4) CC.8.F.1

CC.8.EE.7

(5) CC.8.F.1,2,4

(5L) CC.8.F.1,2,4,5

CC.8.EE.7

8.1.8.A.5


ordered pair, coordinate plane, x-

axis, y-axis, quadrant, x-coordinate,

y-coordinate, origin, continuous

graph, discrete graph relation,

domain, range, function,

independent variable, dependent

variable, vertical line test


Chapter 2



graphing calculator

Formative:

Observation

Quiz 2A

Quiz 2B

Summative:

Chapter Test 2

42



Grade: 8 Unit: Exponents and Roots (3) Time Frame: 39 periods


Exponents and scientific notation can be used to

describe very large and very small numbers.

The Pythagorean Theorem works “in both

directions” (converse).

How do we simplify expressions involving

exponents?

How do we convert into and out of scientific

notation?

What does take the square root of a number mean?

How can I use the Pythagorean Theorem to find

missing lengths.


Students will know:

the property of integer

exponents to generate

equivalent numerical

expressions.

strategies to estimate very large

or very small numbers, express

numbers in the form of a single

digit, times an integer power of

10.

operations with numbers

expressed in scientific notation.

to choose units of appropriate

size for measurement large and

small.

the square root and cubed root

is undoing a square or cube

number and that √2 is irrational.

to approximate an irrational

number between two perfect

squares.

by applying properties of

integer exponents they will

generate equivalent numerical

expressions.

every number has a decimal

expansion, they terminate,

repeat or end in zero, the others

are irrational.

methods to determine all sides

of a right triangle to prove the

Pythagorean Theorem.


use exponents and scientific

notation to describe numbers.

investigate and apply the


(1) evaluate expressions with

negative exponents and

evaluate the zero exponent.

(2) apply properties of exponents.

(3) express large and small

numbers in scientific notation

and compare two numbers

written in scientific notation.

(4) operate with scientific notation

in real world situations.

(4L) use graphing calculator to

multiple and divide numbers in

scientific notation.

(5) find square roots.

(6) estimate square roots to a given

number of decimal places and

solve problems using square

roots.

(7L) use base 10 blocks to explore

cube roots.

(7L)use a graphing calculator to

evaluate expressions that have

negative exponents.

(7) Determine if a number is

rational or irrational.

(7E) classify numbers as rational or

irrational and graph them on a

number line.

(1) CC.8.EE.1

(2) CC.8.EE.1

(3) CC.8.EE.3,4

(4) CC.8.EE.3,4

(4L) CC.8.EE.4

(5) 8.EE.2

(6) 8.NS.2

(7L) 8.EE.2

(7L) 8.EE.1

8.1.8.A.5

(7) 8.NS.1

8.EE.2

(7E)8.NS.2

43

to find distance between two

points on a coordinate system

using the Pythagorean

Theorem.

(8L) use scissors and paper to

Explore right triangles.

(8) use the Pythagorean Theorem

to solve problems.

(9L) use geometry software to

explore the converse of the


(9) use the Distance Formula and

the Pythagorean and its

converse to solve problems.

(8L) 8.G.6

(8) 8.G.7

8.G.6

(9L)8.G.6

8.1.8.A.5

(9) 8.G.8


scientific notation, square root,

principal square root, perfect

square, irrational number, real

number, density property,

Pythagorean Theorem, leg,

hypotenuse,


Chapter 3


(2,3,7,8,9)


geometry software

graphing calculator

Formative:

Observation

Quiz 3A

Quiz 3B

Summative:

Chapter Test 3

44



Grade: 8 Unit: Ratios, Proportions, and Similarity (4) Time Frame: 24 periods


You can apply proportional reasoning to solve

problems involving mixtures, princes, rates, and

scale.

Defining a ratio as a quotient works for any pair of

real numbers as long as division by zero is

prohibited.

Numerators must represent corresponding side

lengths and that the denominators must represent

corresponding side lengths when writing a

proportion in which each ratios compares side

lengths within on the triangles.

How are ratios and proportions used in relation to

similarity?

How can I solve problems involving ratios and

rates without using a proportion?

How does scale factor relate to similarity in

triangles or quadrilaterals?


Students will know:

a two dimensional figure is

similar to another, if the second

can be obtained from a series of

transformations.

missing sides can be derived

from similar figures.

the effects of all

transformations.


use ratio and proportionality to

solve problems.

apply reasoning about similar

triangles to solve problems.

(1) work with rates and ratios.

(2) solve proportions.

(3L) use a number cube and graph

paper to explore similarity.

(3) determine whether figures are

similar and find missing

dimensions.

(4L) use graph paper and a ruler to

explore dilations of geometric

figures.

(4) identify and create dilations of

plane figures.

(3L) 8.G.4

(3) 8.G.4

(4L) 8.G.3

(4) 8.G.4

8.G.3


rate, unit rate, unit price, cross

products, similar, corresponding

sides, corresponding angles,

dilations


Chapter 4



graph paper, number cubes, metric

ruler, protractors

Formative:

Observation

Quiz 4A

Quiz 4B

Summative:

Chapter 4 Test

45



Grade: 8 Unit: Geometric Relationships (5) Time Frame: 45 periods


An understanding of angles, lines, and geometric

relationships is essential for many careers and

hobbies.

There are various ways to prove that two lines are

parallel.

The sum of the measures of the exterior angles of a

polygon is always 360°.

The Distance Formula can be used to determine

whether sides of polygons in a coordinate plane are

congruent.

The image of any figure under a translation,

reflections, or rotation is congruent to the original

figure (pre-image).

How are angles of intersecting lines related?

How do parallel lines affect angle relationship?

How do we geometrically show solutions to

problems?


Students will know:

angles are measured in degrees.

angles can be grouped or

classified by measure.

facts about specific lines,

parallel and perpendicular and

will be able to discuss features

including transversals.

informal arguments and proofs

concerning angle sum,

transversals, similarity.

a two dimensional figure is

similar to another, if the 2nd

can

be obtained from a series of

transformations.

verify properties of

transformations.

the effects of dilation,

translation, rotation, and

reflection.


describe two-dimensional

figures.

analyze angles created when a

transversal cuts parallel lines.

find unknown angle measures.

(1) classify angles and find their

measures.

(2L)use a compass and straightedge

to bisect line segments and

angles.

(2) identify parallel and

perpendicular lines and the

angles formed by a transversal.

(3) find unknown angles and

identify possible side lengths in

triangles.

(4L)use geometry software to study

the exterior angles of a

polygon.

(4) identify polygons and

midpoints of segments in the

coordinate plane.

(5L)learn about congruence by

seeing that slides, turns, and

flips do not change the size or

shape of a figure.

(2) 8.G.5

(3) 8.G.5

(4L)8.G.5

8.1.8.A.5

(5L)8.G.1

8.G.2

46

(5) use properties of congruent

figures to solve problems.

(6) transform plane figures using

translations, rotations, and

reflections.

(7) identify transformations as

similarity of congruence

transformations.

(7L) use pattern blocks and a

coordinate plane to explore

compound transformations.

(8) identify the image of a figure

after a combined transformation

is performed, and determine

whether the final image is

similar or congruent to the

original.

(5) 8.G.2

(6) 8.G.1

8.G.2

8.G.3

(7) 8.G.3

8.G.1a-d

(7L)8.G.2

8.G.1

8.G.3

(8) 8.G.3

8.G.2

8.G.4


correspondence, congruent figures,

transformation, image, translation,

reflection, rotation, center of

rotation, similarity transformation,

congruence transformation, image

vs original, similar vs congruent


Chapter 5


(3,4,5,6,7,8)


geometry software, graph paper

Formative:

Observation

Quiz 5A

Quiz 5B

Summative:

Chapter 5 Test

47



Grade: 8 Unit: Measurement & Geometry (6) Time Frame: 27 periods


Pi is the value of the circumference of a circle

divided by its diameter.

Volumes of pyramids and cones are related to the

volumes of prisms and cylinders.

Both the volume formula and the surface area

formula for spheres involve the radius.

How do you find circumference?

How can you use deductive reasoning to find the

perimeter, area, and volume of geometric shapes?


Students will know:

relationships of circumference,

area of circles.

the concept of volume.

formulas of cone, sphere, and

volume help solve real world

problems.

relationships between volumes

of pyramids and prisms and the

relationship between volume of

cone and cylinders.

method of solving linear

equations.

square root and cube root

symbols represent solutions to

equations x2=P, x

3=P.

small perfect squares

√2 is irrational.


analyze figures in two and three

dimensions.

use fundamental geometric

facts to solve problems.

(1L)use a ruler and string to

measure circles.

(1) find the circumference and area

of circles.

(2L)use empty cartons and cans to

explore volume of prisms and

cylinders.

(2) find the volume of prisms and

cylinders.

(3L)use models to explore the

relationship between the

volume of pyramids and

prisms and the relationship

between the volumes of cones

and cylinders.

(3) find the volume of pyramids

and cones.

(4) find the volume and surface

area of spheres.

(2L)8.G.9

(2) 8.G.9

(3L)8.G.9

(3) 8.G.9

8.EE.7

(4) 8.G.9

8.EE.2


circle, radius, diameter,

circumference, volume, prism,

cylinder, cone, pyramid, sphere,

hemisphere, great circle (caution:

books uses ‘edge’→use ‘surface’)


Chapter 6


(1,2,3,4)


ruler, string, various containers

Formative:

Observation

Quiz 6A

Quiz 6B

Summative:

Chapter 6 Test

48



Grade: 8 Unit: Multi-Step Equations (7) Time Frame: 26 periods


A system of equations is a set of two or more

equations that each involve the same set of two or

more variables.

They are several ways to solve a system of

equations.

How do we solve one and two step inequalities

with one variable?

How do you know your solution is correct?

How do you know you are using an efficient

strategy?


Students will know:

rules for combining like terms.

rules for solving one step

equations.

rules for solving linear

equations with rational

coefficients including

distributive property and

combining like terms.

rules for solving equations with

variables on both sides of an

equation.


use equations to analyze and

solve problems.

solve systems of two linear

equations in two variables.

(1) combine like terms in an

expression.

(2) solve multi-step equations.

(3L)use algebra tiles to model

equations with variables on

both sides.

(3) solve equations with variables

on both sides of the equal sign.

(3E)identify one-variable equations

that have one solution,

infinitely many solutions, or no

solutions.

(4) solve systems of equations.

(1) 8.EE.7

(2) 8.EE.7

8.EE.7b

(3L)8.EE.7

8.EE.7a-b

(3) 8.EE.7

8.EE.7a-b

(3E)8.EE.7

8.EE.7a

(4) 8.EE.8

8.EE.7

8.EE.8b-c


terms, like terms, equivalent

expressions, simplify, literal

equations (verbal), solution of a

system of equations.


Chapter 7



algebra tiles

Formative:

Observation

Quiz 7

Summative:

Chapter 7 Test

49



Grade: 8 Unit: Graphing Lines (8) Time Frame: 36 periods


Graphs of linear equations can be used to display

speeds, distances, and other transportation

situations.

Lines with a slope of zero do have slopes.

Direct variations model a wide range of situations,

including measurement conversions and many

geometric relationships.

How do you graph linear equations?

How can you look at a graph and find its slope and

intercepts?

How do we interpret the slope of a line?


Students will know:

qualitatively the functional

relationship between 2

quantities by analyzing a graph.

the model of functions is a

linear relationship between two

quantities.

how to determine an interpret

rate of change.

similar triangles explain slope

and rate of change (fractions in

simplest form).


be described by difference in

slope.

y = mx + b can be interpreted

as a linear function.


to each input exactly one

output.

the procedure to solve systems

(pairs of linear equations).

the solution of a system is a

point of intersection.

solving systems by graphing

can be estimated.


understand that the slope of a

line is a constant rate of change.

describe aspects of linear

equations in different

representations.

(1) identify and graph linear

equations.

(2L) use points on the graph of a

line and right triangles to

explore the slope of a line.

(2) find the slope of a line and use

slope to understand and draw

graphs.

(3) use slopes and intercepts to

graph linear equations.

(3L)use a graphing calculator to

graph equations in slope-

intercept form.

(4) find the equation of a line given

one point and the slope.

(5) recognize direct variation by

graphing tables of data and

checking for constant ratios.

(6) graph and solve systems of

linear equations.

(1) 8.F.5

8.F.4

(2L) 8.EE.6

(2) 8.EE.5

(3) 8.F.4

(3L) 8.F.3

(4) 8.F.4

(5) 8.F.5

8.F.1

(6) 8.EE.8a

8.EE.8b

8.EE.8c


linear equation, rate of change,

slope, rise, run, x intercept, y

intercept, slope-intercept form,

direct variation, constant of

variation, systems


Chapter 8



Formative:

Observation

Quiz 8A

Quiz 8B

Summative:

Chapter 8 Test

50



Grade: 8 Unit: Data, Prediction, and Linear Functions (9) Time Frame: 33 periods


Predictions can be made from models developed

from data.

A scatter plot shows all the collected data and it is

meaningless too draw a jagged path connecting the

points.

Drawing a line of best fit offers a straightforward

way to predict data values that may not be

displayed on the graph.

How do we find the relationship of a scatter plot?

How do we create a table of values and then write

its equation?

How do different data set representation relate to

each other?


Students will know:

construction and interpretation

of scatter plots.

straight lines are used to model

relationships between two

quantities.

scatter plot classifications and

have ability to make

predictions.


one output to each input.

a function will model a linear

relationship.

functions can be represented in

many different ways:

algebraically, graphically,

numerically, and verbally.

unit rate is slope~, it is the

comparison of proportional

relationships.


use models for data to make

predictions.

Identify, write, and use

linear functions.

(1) create and interpret scatter

plots.

(2) identify patterns in scatter plots,

and informally fit and use a

linear model to solve problems

and make predictions as

appropriate.


make a scatter plot.

(3) identify and write linear

functions.

(4) compare linear functions

represented in different ways.

(1) 8.SP.1

8.SP.2

(2) 8.SP.3

8.SP.1

8.SP.2

(2L) 8.SP.2

8.SP.2

8.1.8.A.5

(3) 8.F.1

8.F.4

8.F.3

(4) 8.F.2

8.EE.5

8.F.4


scatter plot, correlation, line of best

fit, linear function, function

notation


Chapter 9



graphing calculator, graph paper,

Tech Lab materials

Formative:

Observation

Quiz 9A

Quiz 9 B

Summative:

Chapter 9 Test

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